- The two panels of
Figure 30 show a comparison of
the Virgo and Fornax clusters of
galaxies drawn to scale, as seen projected on the sky. The comparison
of apparent sizes is appropriate given that the two clusters are at
approximately the same distance from us. In the extensive Virgo cluster (right panel), the galaxy M100 can be
seen marked ~ 4
degrees to the north-west of the elliptical-galaxy-rich core; this
corresponds to an impact parameter of 1.3 Mpc, or 8% of the distance
from the LG to the Virgo cluster. The Fornax cluster (left panel) is
more centrally concentrated than Virgo, so that the back-to-front
uncertainty associated with its three-dimensional spatial extent is
reduced for any randomly selected member. Roughly speaking,
converting the total angular extent of the cluster on the sky (~ 3
degrees in diameter (7)) into a back-to-front extent, the error
associated with any randomly chosen galaxy in the Fornax cluster,
translates into a few percent uncertainty in distance; and that
uncertainty in distance will soon be reduced when the two additional
Fornax spirals are observed with HST in the coming
year.

Velocity

- Here, we note that the infall-velocity
correction for the Local Group motion with respect to the Virgo cluster (and its associated uncertainty)
becomes a minor issue for the
Fornax cluster. This is the result of a fortuitous
combination of
geometry and physics. We now have Cepheid distances from the Local
Group to both Fornax and Virgo. Combined with their angular
separation on the sky this immediately leads to the physical
separation between the two clusters proper. Under the assumption that
the Virgo cluster dominates the local velocity
perturbation field at the Local Group and at Fornax, we can calculate the velocity
perturbation at Fornax (assuming that the flow field amplitude scales
with 1/ RVirgo and characterized by a
R-2 density distribution
(Schechter 1980).
From this we then derive the flow
contribution to the measured line-of-sight radial velocity, as seen
from the Local Group. Figure 33 shows the
distance scale structure
(left panel) and the velocity-field geometry (right panel) of the
Local Group-Virgo-Fornax system. Adopting an infall velocity of the
Local Group toward Virgo of +200 km/sec (10) with an uncertainty of
± 100 km/sec, the flow correction for Fornax is only -44
± 22 km/sec.

Figure 33. Relative geometry (left
panel), and the
corresponding velocity vectors (right panel) for the disposition and
flow of Fornax and the Local Group with respect to the Virgo cluster. The circles plotted at the positions
of the Virgo and Fornax
clusters have the same angular size as the circles minimally enclosing
M100 and NGC 1365 in the two panels of
Figure 30.

-
Correcting to the barycentre of the Local Group (-90 km/sec) and
compensating for the -44 km/sec component of the Virgocentric flow,
derived above, we calculate that the cosmological expansion rate of
Fornax is 1,321 km/sec. Using our Cepheid distance
of 18.0 Mpc for
Fornax gives H0 = 73 (±
7)r
[± 20]s km/sec/Mpc. The first
uncertainty (in parentheses) includes random errors in the distance
derived from the PL fit to the Cepheid data, as well as random
velocity errors in the adopted Virgocentric flow, combined with the
distance uncertainties to Virgo propagated through the flow model.
The second uncertainty (in square brackets) quantifies the currently
identifiable systematic errors associated with the adopted mean
velocity of Fornax, and the adopted zero point of the PL
relation
(combining in quadrature the LMC distance error, a measure of the
metallicity uncertainty, and a generous estimate of the possible
differences in the true modulus that might be generated from adopting
different stellar photometry packages). Finally, we note that
according to the Han-Mould model
(Han & Mould 1990),
the so-called
``Local Anomaly'' gives the Local Group an extra velocity component of
approximately +73 km/sec towards Fornax. If we were to add that
correction our local estimate, the Hubble constant would increase to
H0 = 77 km/sec/Mpc.

Given the highly clumped nature of the local universe and the
existence of large-scale streaming velocities, there is still a
lingering uncertainty about the total peculiar motion of the Fornax cluster with respect to the cosmic microwave
background restframe.
Observations of flows, and the determination of the absolute motion of
the Milky Way with respect to the background radiation suggest that
line-of sight velocities ~ 300 km/sec are not uncommon
(Coles & Lucchin 1995).
The uncertainty in absolute motion of Fornax with
respect to the Local Group then becomes the largest outstanding
uncertainty at this point in our error analysis: a 300 km/sec flow
velocity for Fornax would result in a systematic error in the
Hubble
constant of ~ 20%. We shall however be able to look from afar,
and revisit this issue, following an analysis of more distant galaxies
made later in this section.